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Mathematics
Mathematics
Problem
Find
∫
d
x
x
2
+
a
2
\displaystyle \int \frac{dx}{\sqrt{x^{2}+a^{2}}}
∫
x
2
+
a
2
d
x
, where
a
>
0
a>0
a
>
0
. a)
1
a
tan
−
1
(
x
a
)
+
C
\dfrac{1}{a}\tan^{-1}\!\left(\dfrac{x}{a}\right)+C
a
1
tan
−
1
(
a
x
)
+
C
b)
x
x
2
+
a
2
+
C
\dfrac{x}{\sqrt{x^{2}+a^{2}}}+C
x
2
+
a
2
x
+
C
c)
ln
∣
x
+
x
2
+
a
2
∣
+
C
\ln|x+\sqrt{x^{2}+a^{2}}|+C
ln
∣
x
+
x
2
+
a
2
∣
+
C
d)
sin
−
1
(
x
a
)
+
C
\sin^{-1}\!\left(\dfrac{x}{a}\right)+C
sin
−
1
(
a
x
)
+
C
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